The rescue disk is unique to each system but the answer to whether you will be able to use it is maybe.
The rescue disk has several purposes. One of those purposes is to provide a backup of the master key for the encrypted volume. The master key is unique to each encrypted volume, even if two encrypted volumes have the same password, they will have different master keys - the master key is actually stored in the volume header and the password is used to decrypt it.
Restoring a master key from a different encrypted volume to that drive would render it unreadable.
The rescue disk still has usable tools to repair the bootloader, and to decrypt the drive if the master key is still intact on it, but the safest option here would be to simply use the desktop TrueCrypt application to decrypt it - which should be possible so long as the password is still known and the master key for it hasn't been damaged. Doing it this way will prevent you from accidentally restoring the other volume's master key during the recovery process. You can test whether this will work without risking any data loss by simply trying to mount that disk with the correct password in the TrueCrypt application.
http://www.truecrypt.org/docs/rescue-disk has a little more detail about the rescue disk functionality.